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Magnetic fields play a fundamental role for interior and atmospheric properties of M dwarfs and greatly influence terrestrial planets orbiting in the habitable zones of these low-mass stars. Determination of the strength and topology of magnetic fields, both on stellar surfaces and throughout the extended stellar magnetospheres, is a key ingredient for advancing stellar and planetary science. In this talk I will review modern methods of magnetic field measurements applied to M dwarfs, with an emphasis on direct diagnostics based on interpretation of the Zeeman effect signatures in high-resolution intensity and polarization spectra. I will summarize results of total field strength measurements derived from Zeeman broadening analyses as well as information on global magnetic geometries inferred with Zeeman Doppler imaging. The emerging understanding of complex, multi-scale nature of M-dwarf magnetic fields is discussed in the context of theoretical models of hydromagnetic dynamos.

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